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CATEGORIES:Topology and Dynamics seminar
SUMMARY:Geometric functionals of fractal percolation - Ste
ffen Winter (KIT)
DTSTART:20211118T150000Z
DTEND:20211118T160000Z
UID:TALK5104AT
URL:/talk/index/5104
DESCRIPTION:Fractal percolation is a family of random self-sim
ilar sets suggested by Mandelbrot in the seventies
to model certain aspects of turbulence. It exhibi
ts a dramatic topological phase transition\, chang
ing abruptly from a dust-like structure to the app
earance of a system spanning cluster. The transiti
on points are unknown and difficult to estimate\,
and beyond the fractal dimension not so much is kn
own about the geometry of these sets. It is a natu
ral question whether geometric functionals such as
intrinsic volumes can provide further insights.\n
\nWe study some geometric functionals of the fract
al percolation process *F*\, which arise as
suitably rescaled limits of intrinsic volumes of
finite approximations of *F*. We establish
the almost sure existence of these limit functiona
ls\, clarify their structure and obtain explicit f
ormulas for their expectations and variances as we
ll as for their finite approximations. The approac
h is similar to fractal curvatures but in contrast
the new functionals can be determined explicitly
and approximated well from simulations. Joint work
with M. Klatt.
LOCATION:Zoom
CONTACT:David Craven
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